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ThisSpaceAvailable comments on FiveThirtyEight (Nate Silver) rolls out new blog today, and attempts to teach people Bayes' rule. - Less Wrong
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Comments (10)
If you're just looking at the study, then it's quite difficult for the support ratio to be less than one. However, suppose we assume that on average, for every published study, there are 100 unpublished studies, and the one with the lowest p-value gets published. Then if a study has a p-value of .04, that particular study supports the headline. However, the fact that that study was published contradicts the headline: if the headline were true, we would expect the lowest p-value to be lower than .04.
Yes, that's what I meant by "very rare:" there are situations where it happens, like the model that you gave, but I don't think ones that happen in real life likely to contribute a very large effect. You need really insane publication bias to get a large effect there.